Notes from the International Autumn School on Computational Number Theory (Tutorials, Schools, and Workshops in the Mathematical Sciences)

Inam, Ilker (EDT)/ Büyükaşık, Engin (EDT)

Springer Nature Switzerland AG（2019/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 363 p.
• 言語 ENG
• 商品コード 9783030125578

Full Description

This volume collects lecture notes and research articles from the International Autumn School on Computational Number Theory, which was held at the Izmir Institute of Technology from October 30th to November 3rd, 2017 in Izmir, Turkey. Written by experts in computational number theory, the chapters cover a variety of the most important aspects of the field. By including timely research and survey articles, the text also helps pave a path to future advancements. Topics include:

Modular forms

L-functions

The modular symbols algorithm

Diophantine equations

Nullstellensatz

Eisenstein series

Notes from the International Autumn School on Computational Number Theory will offer graduate students an invaluable introduction to computational number theory. In addition, it provides the state-of-the-art of the field, and will thus be of interest to researchers interested in the field aswell.

Contents

Part I: Lecture Notes.- An Introduction to Modular Forms.- Computational Arithmetic of Modular Forms.- Computational Number Theory in Relation with L-functions.- Exponential Diophantine Equations.- Part II: Research Contributions.- Nullstellensatz via Nonstandard Methods.- On the (1 + u2 + u3)-Constacyclic and cyclic codes over the finite ring F2 + uF2 + u2F2 + u3F2 + vF2.- On higher congruences between cusp forms and Eisenstein series.- Lucas Numbers which are Products of Two Balancing Numbers.